Question

The dimensional formula of $\frac{B^2}{2\mu_0}$ is ______.

• A. $M^1 L^{-1} T^{-2}$
• B. $M^0 L^{-1} T^{-2}$
• C. $M^1 L^2 T^{-2}$
• D. $M^1 L^1 T^{-2}$

Hint:

Magnetic energy density ($\frac{B^2}{2\mu_0}$) and Electrostatic energy density ($\frac{1}{2}\varepsilon_0 E^2$) have the \textbf{same} dimensions because they both represent energy per unit volume.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The expression $\frac{B^2}{2\mu_0}$ represents the magnetic energy density (energy per unit volume) stored in a magnetic field.
Step 2: Dimensional Analysis:
Energy Density = $\frac{\text{Energy}}{\text{Volume}}$
Dimensions of Energy = $[M^1 L^2 T^{-2}]$
Dimensions of Volume = $[L^3]$
$$\text{Dimensions of Energy Density} = \frac{M^1 L^2 T^{-2}}{L^3} = [M^1 L^{-1} T^{-2}]$$
Step 3: Final Answer:
The correct option is (a).